Sebastian Xambó Descamps
Using intersection theory (EN)
Sociedad Matemática Mexicana, 1996. 122 p. ISBN: 968-36-3591-1 (Aportaciones Matemáticas, Nivel Avanzado, 7).

Contents

0. Introduction. Acknowledgements. Notations, conventions and terminology. Motivating examples: Bézout's theorem and Plücker's formulas.
1. Intersection rings. Cycles and intersections. Action of mappings on cycles. Chow groups and intersection rings. Computing Chow groups; Bézout's theorem. Concluding remarks.
2. Chern classes. Axioms. Calculating Chern classes directly from the axioms. Calculating Chern classes using the splitting principle. Example: The bundle E_d,m. Riemann−Roch.
3. Projective bundles. The intersection ring of a projective bundle. Existence and uniqueness of Chern classes. Example: The intersection ring of X_d,m=P(E_d,m).
4. Grassmannians. Schubert conditions. The intersection ring of Gr(1,n). Tautological bundles. Linear spaces contained in a hypersurface.
5. Flag varieties. Flags in P² and in P³. Grothendieck's description. On Monk's presentation.
6. Characteristic numbers. Conormal variety and contact conditions. Characteristic numbers and the contact theorem. Characteristic numbers of twisted cubics.
7. Rational equivalence on a blow-up. Preliminaries. Chow groups of a blow-up. Intersections on a blow-up.
8. Complete quadrics. Point and line conics. Complete conics. Quadrics in P³: characteristic numbers.

• MR1649152 (99j:14005)
• Publisher's book page

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© S. Xambó
Last update: 17/07/2012